"I think she's done a serviceable job," Trump said in an interview published late on Tuesday, as the billionaire real estate mogul moved a step closer to becoming his party's nominee with a resounding win in the New York state nominating contest.
"I don't want to comment on reappointment, but I would be more inclined to put other people in."
Yellen was nominated for the top Fed job by Democratic President Barack Obama and began her four-year term in February 2014.
In his interview, Trump said he "absolutely" backed efforts to diminish the Fed's power and allow Congress to audit it, and backed away from his pledge to erase the more than $19 trillion in U.S. debt in eight years.
Representatives for the Fed declined to comment on the report.
Trump said he favored the low interest rate environment and that raising rates would be a blow to the U.S. economy. Trump had accused the Fed in November of keeping rates low to help Obama, an assertion the White House rejected.
"The best thing we have going for us is that interest rates are so low," Trump told Fortune.
"If rates are 3 percent or 4 percent or whatever, you start adding that kind of number to an already reasonably crippled economy in terms of what we produce, that number is a very scary number," he added.
The Fed cut its key overnight lending rate to near zero in late 2008 and kept it there for the next seven years to help the economy recover from the financial crisis. It raised rates by a quarter of a percentage point last December, its first hike in nearly a decade.
Trump told Fortune he would take advantage of lower rates to refinance the country's debt and boost government spending on infrastructure and the military. The magazine will publish a full transcript of the interview later this week.
He moved away from comments he made to the Washington Post earlier this month pledging to eliminate the national debt "over a period of eight years."
Instead, Trump told Fortune he could tackle a portion of it.
"You could pay off a percentage of it, depending on how aggressive you want to be," he said. "I'd rather not be all that aggressive. I'd rather not have debt, but we’re stuck with it."
Trump's main Republican rival, U.S. Senator Ted Cruz of Texas, has said he would audit the Fed and move it to a rules-based monetary policy.
Other U.S. presidential candidates, including Democrat Bernie Sanders, have also pledged to change the Fed.